Calculate elevator acceleration from cable force, apparent weight, or speed change using mass, gravity, time, and unit conversions.
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Elevator Acceleration Formula
The calculator uses one of three formulas depending on which calculation you select. All results are returned in m/s², with conversions to ft/s² and g.
Cable force mode:
Scale reading mode:
Speed change mode:
- a = elevator acceleration (m/s²). Positive is upward.
- T = upward cable or motor tension (N)
- m = mass of the elevator car plus its load (kg)
- g = acceleration due to gravity (m/s²), default 9.80665
- F_scale = apparent weight read on a scale inside the car (N)
- v_i, v_f = initial and final velocity (m/s)
- t = time taken for the velocity change (s)
The cable force calculation applies Newton’s second law to the car: the net upward force is T minus the weight mg, divided by the mass. The scale reading calculation uses the same logic from the rider’s perspective, where the scale reads m(g+a). The velocity change calculation skips forces entirely and uses the kinematic definition of average acceleration.
Illustrative Values and Result Interpretation
These illustrative values show the scale of acceleration; the configuration labels are examples, not verified typical ranges or comfort/safety limits. The sign table describes the ideal force model.
| Illustrative case | Example acceleration | In g |
|---|---|---|
| Example A | 0.6 to 0.9 m/s² | 0.06 to 0.09 g |
| Example B | 1.0 to 1.2 m/s² | 0.10 to 0.12 g |
| Example C | 1.5 to 2.0 m/s² | 0.15 to 0.20 g |
| Example D | 2.0 to 2.5 m/s² | 0.20 to 0.25 g |
| Ideal free fall (no support) | -9.81 m/s² | -1.00 g |
| Sign of a | What it means | Apparent weight |
|---|---|---|
| a > 0 | Accelerating up or slowing down while descending | Heavier than mg |
| a = 0 | At rest or constant speed | Equal to mg |
| a < 0 | Accelerating down or slowing while rising | Lighter than mg |
| a = -g | Free fall | Zero (weightless) |
Example Problems
Example 1: Cable tension. An elevator car with passengers has a mass of 800 kg. The cable pulls upward with 8,400 N. Using a = T/m – g:
a = 8400 / 800 – 9.81 = 10.5 – 9.81 = 0.69 m/s². The car accelerates upward at about 0.07 g.
Example 2: Bathroom scale in an elevator. A 70 kg person stands on a scale that reads 770 N. Using a = F/m – g:
a = 770 / 70 – 9.81 = 11.0 – 9.81 = 1.19 m/s² upward. If the same scale read 630 N, the acceleration would be -0.81 m/s², meaning the elevator is accelerating downward.
FAQ
Why is my acceleration negative? Negative means the acceleration vector points downward. This happens when the elevator starts moving down, when it slows to a stop at the top floor, or when the cable tension is less than the car’s weight.
What gravity value should I use? The default 9.80665 m/s² is standard gravity. Use the gravity specified by your problem when available. Changing the unit converts the value; standard gravity is approximately 32.17405 ft/s².
Does the cable force include the counterweight? T is the total upward support force applied to the car, excluding gravity. It is not the net force after subtracting weight or a motor rating. A real counterweighted system requires its actual car support force and any other vertical forces to be accounted for.
How is apparent weight related to acceleration? A scale reads the normal force pushing up on the rider, which equals m(g+a). If a is positive the scale reads more than your true weight; if a is negative it reads less. At a = -g the scale reads zero.
